MinT - Best Known (23, 23+81, s)-Nets in Base 32

Best Known (23, 23+81, s)-Nets in Base 32

(23, 23+81, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 104, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 104, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(23, 23+81, 128)-Net in Base 32 — Constructive

(23, 104, 128)-net in base 32, using

4 times m-reduction [i] based on (23, 108, 128)-net in base 32, using
- base change [i] based on digital (5, 90, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(23, 23+81, 185)-Net over F₃₂ — Digital

Digital (23, 104, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 104, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(23, 23+81, 3800)-Net in Base 32 — Upper bound on s

There is no (23, 104, 3801)-net in base 32, because

1 times m-reduction [i] would yield (23, 103, 3801)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107990 839285 237448 555275 400562 216215 286015 835743 349489 128180 514474 840470 584640 713081 379416 457041 558009 092824 304997 517567 824517 579218 983548 848689 691446 857122 > 32¹⁰³ [i]